[R] Drawing random numbers from Uniform distribution with infinite range

[Richard O'Keefe]

Let's look at something that *would* work if it were not that IEEE
doubles are relatively small discrete set,.

Suppose we had two things.
- a U(0,1) uniform random generator able to generate any *real* in the
range 0 .. 1
- an implementation of atanh() that works for any real in the range 0
.. 1 and can return any real number.
Then atanh(runif(n)*2 - 1) would do pretty much what you want,.
Try it in R.
f <- function (n = 1000000) atanh(runif(n)*2 - 1)
summary(f())
It turns out that working with *representable* numbers means that the
results of f() are limited to
roughly -18,.4 to 18.4, and with n = 1000000 the extremes are almost
always around 7.
Something that, for actual real numbers, could return *any* real, for
representable numbers
can only return -18-and-a-bit to +18-and-a-bit.

This suggests a completely different approach to your original
problem, whatever it is.
Instead of working with the entire real line, transform your problem
to work with the interval (0,1).

On Tue, 29 Jul 2025 at 04:01, Daniel Lobo <danielobo9976 using gmail.com> wrote:
>
> Hi,
>
> I want to draw a set of random number from Uniform distribution where
> Support is the entire Real line.
>
> runif(4, min = -Inf, max = Inf)
>
> However it produces all NAN
>
> Could you please help with the right approach?
>
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